Measurement system fleet optimization

ABSTRACT

A method, system and program product are disclosed for optimizing a fleet of measurement systems. One embodiment determines a tool matching precision (TMP) and a fleet measurement precision (FMP) and normalizes these metrics across applications. An optimization is carried out in which usage weighting factors are assigned to each measurement system while enforcing usage enforcement rule(s) to ensure that each measurement system is optimally used and each application is adequately covered. The optimization re-assigns usage weighting factors to minimize a normalized FMP metric and enforce the usage enforcement rule(s).

BACKGROUND OF THE INVENTION

1. Technical Field

The invention relates generally to manufacturing measurement systemanalysis, and more particularly, to a method, system and program productfor optimizing a fleet of measurement systems.

2. Background Art

Methodologies have been described for the assessment and maintenance ofa fleet of measurement systems or tools within a manufacturer. The focusof these methodologies has been on a fleet of measurement systems for asingle application. While prior approaches use measurement systems as anexample, the methodologies can also be extended to processing equipmentor tools. One approach to assessment includes calculating measurementsystem under test (MSUT) tool matching precision (TMP), in U.S. Ser. No.11/065,740, which is hereby incorporated by reference. Once the TMPs ofa fleet of measurement systems have been determined, then a fleetmeasurement precision (FMP) may be calculated, which is also disclosedin U.S. Ser. No. 11/065,740. Methods to reduce FMP by evaluatingcomponents of variance that comprise each measurement system's TMP mayalso be employed. The above-identified metrics employ two metricsbesides the conventional measures of precision and offset, i.e.,SISoffset and non-linearity. If TMP and/or FMP fail when qualifyingmeasurement systems, these metrics provide guidance on what needs to beaddressed on the MSUT for the given application thereby guiding themetrology engineer on where to start diagnosing for the root cause ofthe matching issue. Techniques for determining a root cause throughnoting which of the four contributors to matching, i.e., precision,offset, SISoffset and non-linearity, is highest, or the combination ofmetrics is highest, may also be employed, as also described in U.S. Ser.No. 11/065,740. A root cause database in which characteristics ofmatching issues are associated with a signature to further refine theroot cause determination may also be employed, as disclosed in U.S. Ser.No. 11/245,865, which is hereby incorporated by reference.

One challenge relative to optimizing a fleet of measurement systems,however, is not having a manner of normalizing different metrics formeasurement systems across different applications for comparison. Inparticular, common practice treats all measurement systems asequivalent, assigning product to measurement systems solely based onavailability. Conventional practices also employ a measurement systemdedication approach in which a measurement system is dedicated to aparticular application. For example, for a particularly challengingapplication, the best measurement system is assigned to be the onlymeasurement system to make the measurements. Historically, the bestmeasurement system was determined based on single measurement systemprecision. Unfortunately, measurement system dedication is inefficientand can actually lead to an overall degradation of the average FMP ofthe fleet across all applications. Having a way to normalize differentmeasurement systems across different applications for comparison andoptimizing the fleet based on the normalized values, therefore, would behelpful.

SUMMARY OF THE INVENTION

A method, system and program product are disclosed for optimizing afleet of measurement systems. One embodiment determines a tool matchingprecision (TMP) and a fleet measurement precision (FMP) and normalizesthese metrics across applications. An optimization is carried out inwhich usage weighting factors are assigned to each measurement systemwhile enforcing usage enforcement rule(s) to ensure that eachmeasurement system is optimally used and each application is adequatelycovered. The optimization re-assigns usage weighting factors to minimizea normalized FMP metric and enforce the usage enforcement rule(s).

A first aspect of the invention provides a method of optimizing a fleetof measurement systems, the method comprising: obtaining an applicationtolerance (T) for each application to which at least one measurementsystem of the fleet is to be exposed; determining a tool matchingprecision (TMP) for each measurement system in the fleet for eachapplication to which a measurement system is exposed; and optimizing thefleet by: a) determining a usage weighting factor (w_(ij)) for eachmeasurement system (i) for each application representative of a time themeasurement system (i) spends performing a particular application (j)and calculating at least one usage enforcement rule, b) calculating aweighted fleet measurement precision (FMP) metric for each applicationto which the fleet is exposed based on the usage weighting factors, theweighted FMP metric equivalent to a root average square of the TMP ofeach measurement system used for the application and weighted based onthe usage weighting factors, c) calculating a normalized FMP metric, thenormalized FMP metric equivalent to a root weighted average square ofthe weighted FMP metric divided by the application tolerance across allapplications, and d) re-assigning the usage weighting factors tominimize the normalized FMP metric for all applications while enforcingthe at least one usage enforcement rule.

A second aspect of the invention provides a system for optimizing afleet of measurement systems, the method comprising: an obtainer forobtaining an application tolerance (T) for each application to which atleast one measurement system of the fleet is to be exposed; a toolmatching precision (TMP) determinator for determining a tool matchingprecision (TMP) for each measurement system in the fleet for eachapplication to which a measurement system is exposed; and an optimizerfor optimizing the fleet, the optimizer including: a) a weight assignerfor determining a usage weighting factor (w_(ij)) for each measurementsystem (i) for each application representative of a time the measurementsystem (i) spends performing a particular application (j) andcalculating at least one usage enforcement rule, b) a fleet measurementprecision (FMP) calculator for: i) calculating a weighted fleetmeasurement precision (FMP) metric for each application to which thefleet is exposed based on the usage weighting factors, the weighted FMPmetric equivalent to a root average square of the TMP of eachmeasurement system used for the application and weighted based on theusage weighting factors, and ii) calculating a normalized FMP metric,the normalized FMP metric equivalent to a root weighted average squareof the weighted FMP metric divided by the application tolerance acrossall applications; and c) a minimizer for invoking the weight assigner tore-assign the usage weighting factors to minimize the normalized FMPmetric for all applications while enforcing the at least one usageenforcement rule.

A third aspect of the invention provides a program product stored on acomputer-readable medium, which when executed, optimizes a fleet ofmeasurement systems, the program product comprising: program code forobtaining an application tolerance (T) for each application to which atleast one measurement system of the fleet is to be exposed; program codefor determining a tool matching precision (TMP) for each measurementsystem in the fleet for each application to which a measurement systemis exposed; and program code for optimizing the fleet, the optimizingprogram code including: a) program code for determining a usageweighting factor (w_(ij)) for each measurement system (i) for eachapplication representative of a time the measurement system (i) spendsperforming a particular application (j) and calculating at least oneusage enforcement rule, b) program code for: i) calculating a weightedfleet measurement precision (FMP) metric for each application to whichthe fleet is exposed based on the usage weighting factors, the weightedFMP metric equivalent to a root average square of the TMP of eachmeasurement system used for the application and weighted based on theusage weighting factors, and ii) calculating a normalized FMP metric,the normalized FMP metric equivalent to a root weighted average squareof the weighted FMP metric divided by the application tolerance acrossall applications; and c) program code for invoking the weight assignerto re-assign the usage weighting factors to minimize the normalized FMPmetric for all applications while enforcing the at least one usageenforcement rule.

A fourth aspect of the invention provides a computer-readable mediumthat includes computer program code to enable a computer infrastructureto optimize a fleet of measurement systems, the computer-readable mediumcomprising computer program code for performing the method steps of theinvention.

An fifth aspect of the invention provides a business method for optimizea fleet of measurement systems, the business method comprising managinga computer infrastructure that performs each of the steps of theinvention; and receiving payment based on the managing step.

A sixth aspect of the invention provides a method of generating a systemfor optimize a fleet of measurement systems, the method comprising:obtaining a computer infrastructure; and deploying means for performingeach of the steps of the invention to the computer infrastructure.

The illustrative aspects of the present invention are designed to solvethe problems herein described and/or other problems not discussed.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features of this invention will be more readilyunderstood from the following detailed description of the variousaspects of the invention taken in conjunction with the accompanyingdrawings that depict various embodiments of the invention, in which:

FIG. 1 shows a block diagram of one embodiment of an optimization systemaccording to the invention.

FIG. 2 shows a flow diagram of one embodiment of an operationalmethodology of the system of FIG. 1.

FIG. 3 shows a flow diagram of one embodiment of an identifier of thesystem of FIG. 1.

It is noted that the drawings of the invention are not to scale. Thedrawings are intended to depict only typical aspects of the invention,and therefore should not be considered as limiting the scope of theinvention. In the drawings, like numbering represents like elementsbetween the drawings.

DETAILED DESCRIPTION

The description includes the following headings for clarity purposesonly: I. Introduction and Definitions, II. System Overview, III.Operational Methodology, and IV. Conclusion.

I. Introduction and Definitions

A method, system and program product for optimizing a fleet ofmeasurement systems are described herein. In one embodiment, theteachings of the invention are applicable to measurement systems. A“measurement system” or “measurement system under test” (hereinafter“MSUT”) (denoted i) can be any tool or group of tools used formeasuring, such as a critical dimension scanning electron microscope, anatomic force microscope, scatterometer, etc. Accordingly, it should berecognized that while particular types of measurement systems may bementioned in the description, the teachings of the invention areapplicable to any type of measurement system. In addition, while theinvention will be described in the setting of the semiconductorindustry, and in particular to critical dimension measurement systems,it should be recognized that the teachings of the invention areapplicable to any industry or measurement system where measurementuncertainty is present and more than one measurement system is used tocontrol a manufacturing setting, e.g., a manufacturing line. Similarly,a “fleet” including at least one measurement system may include avariety of measurement systems. (A fleet may include a mixed fleet ofmultiple generations of tools from the same supplier as well as a fleetof tools from multiple suppliers.) Furthermore, the teachings of theinvention are not limited to measurement systems, and may be applied toany processing or manufacturing measurement systems and/or fleet. As onewith skill in the art will recognize, the metrics disclosed in otherapplications may be modified to accommodate tools other than measurementsystems.

“Application” (j) is one or more situations in which a measurementsystem may be used and is capable of operating.

“Application tolerance” (T) is an acceptable product variation for aparticular application.

“Tool matching precision” (TMP) is a metric that results from aregression analysis that compares measurements from the MSUT and achosen benchmark measurement system (BMS), as defined in U.S. Ser. No.11/065,740. As described therein, in one embodiment, TMP is definedusing this set of parameters as:

${{TMP} = {3\sqrt{\begin{matrix}{{\beta_{MSUT}^{2}\sigma_{MSUT}^{2}} + \left( {{offset} - {offset}_{BMS}} \right)^{2} +} \\{\left( {{SISoffset} - {SISoffset}_{BMS}} \right)^{2} + \sigma_{{non}\text{-}{linearity}}^{2}}\end{matrix}}}},$

where TMP is the tool matching precision, β_(MSUT) is the slope of theMandel regression analysis, σ_(MSUT) is the precision of the MSUT,offset is the average offset (between the MSUT and the BMS),offset_(BMS) is the benchmark measuring system (BMS) average offset(between the BMS and the fleet average), SISoffset is the slope-inducedshift offset, SISoffset_(BMS) is the BMS shift-induced offset, andσ_(non-linearity) is the non-linearity.

“Normalized TMP metric” is a metric to normalize TMP across differentapplications and is equivalent to TMP for a given measurement system (i)for an application (j) divided by the application's tolerance T_(j),i.e., TMP_(ij)/T_(j).

“Fleet measurement precision” (FMP) is a metric that provides anindication of the fleet's overall measurement precision for a givenapplication (j), as defined in U.S. Ser. No. 11/065,740. In that patentapplication, FMP was calculated using equal usage weighting for eachmeasurement system. That is, each measurement system was considered tocarry an equal load.

“Usage weighting factor” (w_(ij)) is a representation of the time themeasurement system (i) spends performing a particular application (j).

“Measurement system weight” (M_(i)) represents a time spent bymeasurement system (i) performing all applications. The measurementsystem weight for measurement system (i) can be calculated according tothe following equation:

$\begin{matrix}{M_{i} = {\sum\limits_{j = 1}^{M}w_{ij}}} & \left( {{Eqn}.\mspace{14mu} 1} \right)\end{matrix}$

In this equation, M is the total number of applications.

“Application weight” (N_(j)) represents a time spent by all measurementssystems performing application (j). The application weight forapplication (j) can be calculated according to the following equation:

$\begin{matrix}{N_{j} = {\sum\limits_{i = 1}^{N}w_{ij}}} & \left( {{Eqn}.\mspace{14mu} 2} \right)\end{matrix}$

In this equation, N is the total number of measurement systems in thefleet

“Weighted FMP metric” is a metric that provides an indication of thefleet's overall measurement precision for a given application (j) basedon usage weighting factors. The weighted FMP metric can be calculatedaccording to the following equation:

$\begin{matrix}{{FMP}_{j} = \sqrt{\frac{1}{N_{j}}{\sum\limits_{i = 1}^{N}{w_{ij}{TMP}_{ij}^{2}}}}} & \left( {{Eqn}.\mspace{14mu} 3} \right)\end{matrix}$

where FMP_(j) is the weighted FMP metric for application (j), N is thenumber of measurement systems in the fleet, w_(ij) is a usage weightingfactor for measurement system (i) for application (j), and TMP_(ij) is aTMP for measurement system (i) for application (j).

“Weighted normalized TMP metric” represents the relative contribution ofmeasurement system (i) to the weighted FMP metric for application (j),and can be calculated according to the following equation:

$\begin{matrix}{\left( \frac{{TMP}_{ij}}{T_{j}} \right)_{wt} = {\sqrt{w_{ij}}{\frac{{TMP}_{ij}}{T_{j}}.}}} & \left( {{Eqn}.\mspace{14mu} 4} \right)\end{matrix}$

“Normalized FMP metric” is a metric to normalize FMP across differentapplications for the fleet and is equivalent to a root weighted average(mean) square of the weighted FMP metric (FMP_(j)) divided by theapplication tolerance (T_(j)) across all applications. The followingequation represents the normalized FMP metric:

$\begin{matrix}{\left( \frac{FMP}{T} \right)_{ras} = \sqrt{\frac{\sum\limits_{j = 1}^{M}{N_{j}\left( {{FMP}_{j}/T_{j}} \right)}^{2}}{\sum\limits_{j = 1}^{M}N_{j}}}} & \left( {{Eqn}.\mspace{14mu} 5} \right)\end{matrix}$

where (FMP/T)_(ras) is the normalized FMP metric, M is the total numberof applications to which the fleet will be exposed, FMP_(j) is the FMPfor application (j) and T_(j) is the application tolerance forapplication (j).

II. System Overview

Turning to the drawings, FIG. 1 shows an illustrative environment 100for optimizing a fleet of measurement systems. To this extent,environment 100 includes a computer infrastructure 102 that can performthe various process steps described herein for optimizing a fleet ofmeasurement systems. In particular, computer infrastructure 102 is shownincluding a computing device 104 that comprises an optimization system106, which enables computing device 104 to optimize a fleet ofmeasurement systems by performing the process steps of the invention.

Computing device 104 is shown including a memory 112, a processor (PU)114, an input/output (I/O) interface 116, and a bus 118. Further,computing device 104 is shown in communication with an external I/Odevice/resource 120 and a storage system 122. As is known in the art, ingeneral, processor 114 executes computer program code, such asoptimization system 106, that is stored in memory 112 and/or storagesystem 122. While executing computer program code, processor 114 canread and/or write data, such as optimization, to/from memory 112,storage system 122, and/or I/O interface 116. Bus 118 provides acommunications link between each of the components in computing device104. I/O device 120 can comprise any device that enables a user tointeract with computing device 104 or any device that enables computingdevice 104 to communicate with one or more other computing devices.

In any event, computing device 104 can comprise any general purposecomputing article of manufacture capable of executing computer programcode installed by a user (e.g., a personal computer, server, handhelddevice, etc.). However, it is understood that computing device 104 andoptimization system 106 are only representative of various possibleequivalent computing devices that may perform the various process stepsof the invention. To this extent, in other embodiments, computing device104 can comprise any specific purpose computing article of manufacturecomprising hardware and/or computer program code for performing specificfunctions, any computing article of manufacture that comprises acombination of specific purpose and general purpose hardware/software,or the like. In each case, the program code and hardware can be createdusing standard programming and engineering techniques, respectively.

Similarly, computer infrastructure 102 is only illustrative of varioustypes of computer infrastructures for implementing the invention. Forexample, in one embodiment, computer infrastructure 102 comprises two ormore computing devices (e.g., a server cluster) that communicate overany type of wired and/or wireless communications link, such as anetwork, a shared memory, or the like, to perform the various processsteps of the invention. When the communications link comprises anetwork, the network can comprise any combination of one or more typesof networks (e.g., the Internet, a wide area network, a local areanetwork, a virtual private network, etc.). Regardless, communicationsbetween the computing devices may utilize any combination of varioustypes of transmission techniques.

As previously mentioned and discussed further below, optimization system106 enables computing infrastructure 102 to optimize a fleet ofmeasurement systems. To this extent, optimization system 106 is shownincluding an obtainer 130, a TMP calculator 132 and an optimizer 134.Optimizer 134 is shown including a weight assigner 136 having a ruleenforcer 138, a FMP calculator 140, a minimizer 142, an identifier 144and other system components 150. Other system components 150 may includeperipheral functions not expressly described herein, but essential tooptimization system 106 operation. Operation of each of these systems isdiscussed further below. However, it is understood that some of thevarious systems shown in FIG. 1 can be implemented independently,combined, and/or stored in memory for one or more separate computingdevices that are included in computer infrastructure 102. Further, it isunderstood that some of the systems and/or functionality may not beimplemented, or additional systems and/or functionality may be includedas part of environment 100.

III. Operational Methodology

Referring to FIG. 2, one embodiment of an operational methodology willnow be described in conjunction with FIG. 1. It is understood that whilea particular order of functions has been illustrated, the order may bealtered from that shown. In the embodiments described herein, it isassumed that a fleet of N measurement systems is being used for Mapplications.

In S1, obtainer 130 obtains an application tolerance (T_(j)) for eachapplication (j) to which at least one measurement system (i) of thefleet is to be exposed. An application tolerance may be stated in anynow known or later developed fashion, e.g., a percent error, anacceptable plus-minus value, etc. Application tolerances may be obtainedin any now known or later developed fashion, e.g., they may be input bya user, recalled from a database, calculated based on other data, etc.

In S2, TMP calculator 132 determines a TMP for each measurement systemin the fleet for each application to which a measurement system isexposed. As stated above, according to one embodiment, TMP may becalculated as defined in U.S. Ser. No. 11/065,740. As an option, TMPcalculator 132 may also calculate a normalized TMP metric for eachmeasurement system for each application. As stated above, according toone embodiment, the normalized TMP metric is equivalent to TMP for agiven measurement system (i) for an application (j) divided by theapplication's tolerance T_(j), i.e., TMP_(ij)/T_(j). This normalized TMPmetric may be helpful for comparison of TMP across differentapplications, as will be described in more detail below.

The normalized TMP metric may be impacted for a measurement system for aparticular application for two reasons. One reason is differences inperformance, perhaps due to measurement system manufacturing tolerances,perhaps due to different environment settings for the measurementsystems, differences in the aging of component parts, or something else.The second reason for the differences in the normalized TMP metricperformance is measurement assessment uncertainty (also called error).If the measurement assessment error is much larger than the realdifferences in performance, then it is not advisable to adjustmeasurement system usage since the measured differences are not real.This understanding drives the need to ensure that the measurementassessment uncertainty is a small contributor to the distribution of thenormalized TMP metric. When this is the case, measurement systemssituated in the outskirts of the distribution are either truly worse orbetter performers compared to the average for the application.

In S3, optimizer 134 optimizes the fleet. The optimization may becarried out in a number of different ways.

In one embodiment, in S3A(i), weight assigner 136 determines (andassigns) a usage weighting factor (w_(ij)) to each measurement system(i) for each application representative of a time the measurement system(i) spends performing a particular application (j) while (via ruleenforcer 138) calculating (enforcing) at least one usage enforcementrule. Conventionally, FMP was calculated using equal weighting of TMPfor each measurement system. However, this does not address thesituation where other measurement systems pick up the slack for toolsthat are excluded from use or are not used fully. A usage weightingfactor (w_(ij)) of zero for a particular application indicates that ameasurement system is not employed for that particular application.

One challenge relative to calculating the usage weighting factors iswarranting that each measurement system is optimally used and eachapplication is adequately covered. That is, if a measurement system isnot used for a particular application, weight assigner 136 and ruleenforcer 138 should warrant that it is used for other applications forwhich it would be helpful. Furthermore, each application has a coveragerequirement, e.g., to maintain a production rate, quality assurance,etc., which must be met by the fleet of measurement systems. In S3A(ii),rule enforcer 138 calculates (and enforces) at least one enforcementrule that mandates these situations are addressed. In one embodiment,two enforcement (sum) rules may be defined for these weighting factors(w_(ij)). For a measurement system to be properly utilized, the sum ofall of its usage weighting factors (w_(ij)) must equal the measurementsystem weight M_(i). That is:

$\begin{matrix}{{\sum\limits_{j = 1}^{M}w_{ij}} = M_{i}} & \left( {{Eqn}.\mspace{14mu} 1} \right)\end{matrix}$

Enforcement of this enforcement rule ensures that a measurement systemexcluded or not fully employed from an application is not idle, i.e., itis being adequately used for another application, and/or measurementsystems for the application are adequately compensating for the excludedor diminished use measurement system. For an application's need formeasurements to be properly covered, the sum of all of measurementsystem usage weighting factors (w_(ij)) for application (j) must equalthe application weight N_(j), that is:

$\begin{matrix}{{\sum\limits_{i = 1}^{N}w_{ij}} = {N_{j}.}} & \left( {{Eqn}.\mspace{14mu} 2} \right)\end{matrix}$

Enforcement of this enforcement rule ensures that an application's needsare met.

In one embodiment, the usage weighting factor (w_(ij)) is initiallydetermined by measuring the time the measurement system (i) spendsperforming a particular application (j). The measurement system weights(M_(i)) are then calculated according to the following equation:

$\begin{matrix}{M_{i} = {\sum\limits_{j = 1}^{M}w_{ij}}} & \left( {{Eqn}.\mspace{14mu} 1} \right)\end{matrix}$

and the application weights (N_(j)) are calculated according to thefollowing equation:

$\begin{matrix}{N_{j} = {\sum\limits_{i = 1}^{N}{w_{ij}.}}} & \left( {{Eqn}.\mspace{14mu} 2} \right)\end{matrix}$

Although two usage enforcement rules have been illustrated, it isunderstood that other rules may also be employed. For example, anotherusage enforcement rule may mandate that no usage weighting factors thatresult in a normalized FMP metric exceeds a threshold, i.e.,(FMP_(j)/T_(j))_(ras)<threshold.

In S3B(i), FMP calculator 140 calculates a weighted FMP metric for eachapplication to which the fleet is exposed based on the usage weightingfactors (w_(ij)). As stated above, the weighted FMP metric provides anindication of the fleet's overall measurement precision for a givenapplication (j) based on usage weighting factors. The weighted FMPmetric is equivalent to a root average square of the TMP for eachmeasurement system (i) used for application (j) and weighted based on ausage weighting factor. The following equation represents the weightedFMP metric:

$\begin{matrix}{{FMP}_{j} = \sqrt{\frac{1}{N_{j}}{\sum\limits_{i = 1}^{N}{w_{ij}{TMP}_{ij}^{2}}}}} & \left( {{Eqn}.\mspace{14mu} 3} \right)\end{matrix}$

where FMP_(j) is the weighted FMP metric for application (j), N is thenumber of measurement systems in the fleet, w_(ij) is a usage weightingfactor for measurement system (i) for application (j), and TMP_(ij) is aTMP for measurement system (i) for application (j).

In addition, at S3B(ii), FMP calculator 140 calculates a normalized FMPmetric, which normalizes FMP across different applications for thefleet. As noted above, the normalized FMP metric is equivalent to a rootweighted average square of the weighted FMP metric (FMP_(j)) divided bythe application tolerance (T_(j)) across all applications. That is:

$\begin{matrix}{\left( \frac{FMP}{T} \right)_{ras} = {\sqrt{\frac{\sum\limits_{j = 1}^{M}{N_{j}\left( {{FMP}_{j}/T_{j}} \right)}^{2}}{\sum\limits_{j = 1}^{M}N_{j}}}.}} & \left( {{Eqn}.\mspace{14mu} 5} \right)\end{matrix}$

where (FMP/T)_(ras) is the normalized FMP metric, M is the total numberof applications to which the fleet will be exposed, FMP_(j) is the FMPfor application (j), N_(i) is the application weight for application(j), and T_(j) is the application tolerance for application (j).

In step S3C, minimizer 142 re-assigns the usage weighting factors byinvoking weight assigner 136 to minimize the normalized FMP metric forall applications while rule enforcer 138 enforces the at least one usageenforcement rule. In this regard, different combinations of usageweighting factors (w_(ij)) are considered in order to optimize thefleet. The smallest possible value of the normalized FMP metriccorresponds to the optimized weighting combination.

In one embodiment, at S3D, the above-described embodiment may besimplified by identifier 144 identifying at least one ‘exclusionmeasurement system’ to exclude from the fleet based on the normalizedTMP metrics, i.e., by assigning the exclusion measurement system(s) avalue of zero. Although S3D is shown at the end of the above-describedmethodology, the order of functions may vary and the identification mayoccur earlier than indicated. This identification may be carried out ina number of ways. However, the overall effect is that the identificationreduces the computational burden by identifying particular measurementsystems for particular applications, where measurement system exclusionmay have an impact. In this manner, the optimization can be restrictedto explore only usage weighting factors (w_(ij)) not set to zero. In oneembodiment, identifier 144 may identify at least one exclusionmeasurement system based on the at least one exclusion measurementsystem having a substantially dissimilar normalized TMP metric comparedto other measurement systems in the fleet. Based on this identification,weight assigner 136 (with rule enforcer 138) may assign the at least oneexclusion measurement system the usage weighting factor of zero, i.e.,not employ the exclusion measurement system for a particularapplication.

In one embodiment, identifier 144 may implement a significance test toensure that optimization operates only on real differences in thenormalized TMP metric among the measurement systems. In particular, thesignificance test may be implemented by the use of Bartlett's test, asdisclosed in: George Snedecor and William Cochran, Statistical Methods,Iowa State University Press, 1967, pp. 296-298, and Acheson Duncan,Quality Control and Industrial Statistics, Richard D. Irwin, Inc., 1965,pp. 641-644. This statistical test is a strong function of the samplesize used to determine the TMP metric. If all the TMP metrics to betested have the same sample size, the Bartlett test can be bypassed byusing the simpler F-test on the largest and smallest TMP in the fleet,and then the next smallest in an iterative fashion.

In an alternative embodiment, binning may be employed. Binning is aprocess of constructing a discrete set of possible values for thenormalized TMP with separations between adjacent values that is greaterthan the assessment uncertainty. For example, if each normalized TMP isuncertain to +/−1%, then binning may construct bins separated by 2%,such as the sequence 0, 2, 4, 6, 8, 10, etc., and change each determinednormalized TMP value to the nearest bin value.

The following is a simplified example of the above-describedmethodology. Consider a fleet of 10 measurement systems and 5application families, as shown in table 1. An “application family” is agroup of applications that have very similar measurement requirements soa single normalized TMP metric applies to the family. Initially, allmeasurement systems are considered equally good and so are assignedequal weighting factors of one, i.e., unity. This then establishes theenforcement rules as requiring all rows must sum to 10 and all columnsmust sum to 5. As shown in table 1, in this example, all normalized TMPmetric values (TMP/T) are 20% except for two measurement systems:measurement system 5 for application family 3 and measurement system 6for application family 4. Hence, these measurement systems areidentified as exclusion measurement systems. For comparison purposes, aweighted FMP metric (Wt FMP/T) value for each application is calculatedwith equal weighting for all measurement systems, i.e., not employingthe above-described methodology, and is shown in table 1. As indicated,because of the exclusion measurement systems, applications 3 and 4 haveundesirable normalized FMP metric (FMP/T) values. Hence, forapplications 3 and 4, the fleet matching is poor compared to the otherapplications. A normalized FMP metric ((FMP/T)_(ras)) for the fleetacross all applications is 21.1.

TABLE 1 100 * TMP/T Measurement Systems Wt Applications 1 2 3 4 5 6 7 89 10 FMP/T 1 20 20 20 20 20 20 20 20 20 20 20 2 20 20 20 20 20 20 20 2020 20 20 3 20 20 20 20 40 20 20 20 20 20 22.8 4 20 20 20 20 20 40 20 2020 20 22.8 5 20 20 20 20 20 20 20 20 20 20 20 (FMP/T)_(ras) 21.1

The following table of usage weighting factors was calculated to excludethe two measurement systems from the application where each has a largernormalized TMP metric (TMP/T). The weighting factors for the other caseswere chosen to equally weight other applications for the two measurementsystems and then adjust weights for the other eight measurement systemsacross applications to ensure the usage enforcement rules are obeyed.These values are close to what would be achieved if, after excludingeach of the two measurement systems from its problem application,product is sent to measurement systems based on availability.

TABLE 2 Usage Weighting Factors Measurement Systems Applications 1 2 3 45 6 7 8 9 10 Sum 1 0.9 0.9 0.9 0.9 1.3 1.3 0.9 0.9 0.9 0.9 10 2 0.9 0.90.9 0.9 1.3 1.3 0.9 0.9 0.9 0.9 10 3 1.1 1.1 1.1 1.1 0 1.3 1.1 1.1 1.11.1 10 4 1.1 1.1 1.1 1.1 1.3 0 1.1 1.1 1.1 1.1 10 5 0.9 0.9 0.9 0.9 1.31.3 0.9 0.9 0.9 0.9 10 Sum 5 5 5 5 5 5 5 5 5 5

The values in the column and row called “sum” indicates the usageenforcement rules are being obeyed.

The following table calculates the weighted FMP metrics (Wt FMP/T) andthe normalized FMP metric ((FMP/T)_(ras)) for the fleet according to theabove-described methodology.

TABLE 3 Applications Wt FMP/T 1 20 2 20 3 20 4 20 5 20 (FMP/T)_(ras) 20Comparing the results from table 1 and table 3, as a consequence ofexclusion measurement systems' exclusion, the weighted FMP metricsvalues are all acceptable and the overall normalized FMP metric for thefleet across all applications has been lowered as well. It is understoodthat due to the simplicity of this example, where all TMP/T values areequal except for two, that there is not a unique solution. It is notnecessary that there is a unique solution, so long as the optimizationcan find a weighting that significantly improves the overall normalizedFMP.

In an alternative embodiment, at S3D, identifier 144 may implement arepeating identification process. Referring to FIG. 3, in this process,at S10, identifier 144 first identifies a first application having anunacceptable weighted FMP metric (e.g., too high compared to othermeasurement systems) and a target measurement system used for the firstapplication having an unacceptable weighted normalized TMP metric whenmultiplied by a square root of a current usage weighting factor w_(ij).Weight assigner 136 assigns a new usage weighting factor by decreasing acurrent usage weighting factor for the target measurement system for thefirst application by a weighting factor correction fraction, i.e., by afraction of one (unity) or less. Hence, usage of the target measurementsystem is diminished. Next, at S12, identifier 144 identifies a secondapplication for the target measurement system having an acceptablenormalized TMP metric (e.g., within a threshold of other applications)among the applications that the target measurement system performs.Weight assigner 136 adjusts a current usage weighting factor for thetarget measurement system for the second application by adding theweighting factor correction fraction. Hence, the amount by which thetarget measurement system's use was diminished for the first applicationis used for the second application. At S14, identifier 144 identifies atleast one compensating measurement system having a normalized TMP metricthat is acceptable for the first application and a normalized TMP metricthat is higher for the second application. These compensatingmeasurement systems compensate for the target measurement system for thefirst and second application. Weight assigner 136 then distributes theweighting factor correction fraction as additions to the usage weightingfactors for the compensating measurement system(s) for the firstapplication and as subtractions to the usage weighting factors for thecompensating measurement system(s) for the second application. That is,the amount by which the target application is diminished for the firstapplication is assigned to at least one compensating measurement systemfor the first application, and the amount by which the targetmeasurement system usage increases for the second application acts toreduce usage of the compensating measurement systems for the secondapplication. Each usage weighting factor assignment also includes ruleenforcer 138 enforcing the at least one usage enforcement rules. Thisprocess may repeat, as shown in FIG. 3, numerous times until no furtherbenefit results or until the normalized FMP metric goals have been met.

The following example illustrates use of this process. Consider as anexample for illustration a fleet of 10 tools supporting 5 applications.In this example, the weighting factor correction fraction for the targetmeasurement system for the first application is one, i.e., unity. Also,the initial usage weighting factors assume all the tools perform equallywell so the factors are all equal. This is shown in Table 4. These sumsfor the rows and columns in this table establish the enforcement ruleconstraints that must be enforced through each pass of the optimization.Furthermore, the compensating measurements systems total one.

TABLE 4 Initial Usage Weighting Factors Tools Applications 1 2 3 4 5 6 78 9 10 Sum 1 1 1 1 1 1 1 1 1 1 1 10 2 1 1 1 1 1 1 1 1 1 1 10 3 1 1 1 1 11 1 1 1 1 10 4 1 1 1 1 1 1 1 1 1 1 10 5 1 1 1 1 1 1 1 1 1 1 10 Sum 5 5 55 5 5 5 5 5 5

Further consider as an example for illustration the set of normalizedTMP metrics (TMP/T) generated by a random number generator to produce auniform distribution from 10 to 30 shown in Table 5.

TABLE 5 100 * TMP/T Tools Applications 1 2 3 4 5 6 7 8 9 10 1 18 12 2228 28 29 10 18 27 13 2 15 11 11 13 14 10 16 17  21* 17 3 17 17 28 19 1916 30 26 30 15 4 29 11 24 26 29 19 16 25  17* 26 5 11 14 11 17 20 20 1730 11 15Note that the TMP/T values are listed as percent. Using the usageweighting factors of Table 4 and the TMP/T values of Table 5, theweighted FMP/T values for all applications can be calculated accordingto Eqn. 3 and the normalized FMP for the fleet can be calculatedaccording to Eqn. 5. These are given in Table 6.

TABLE 6 Initial FMP Results Applications FMP/T 1 21.64 2 14.86 3 22.45 422.94 5 17.50 (FMP/T)_(ras) 20.13Executing the above-described embodiment, referring to FIG. 3, in S10,identifier 144 identifies measurement system 5 as a target measurementsystem by application 4 and decreases the current usage weighting factorby a weighting factor correction fraction. In this case, it is decreasedto zero. At S12, identifier 144 identifies application 2 for targetmeasurement system 5 and increases the current usage weighting factor bya weighting factor correction fraction, here 1. In this case, the usageweighting factor for measurement system 5 for application 2 is increasedto 2. At S14, identifier 144 identifies measurement system 9 byapplications 2 and 4 as a compensating measurement system forrebalancing the usage weighting factors that were set to 0 and 2,respectively. These selections are illustrated with an asterisk in Table5. The resulting distribution of the weighting factor correctionfraction as additions to the usage weighting factors for thecompensating measurement system(s) for the first application and assubtractions to the usage weighting factors for the compensatingmeasurement system(s) for the second application is shown in Table 7.

TABLE 7 First Pass Usage Weighting Factors Tools Applications 1 2 3 4 56 7 8 9 10 Sum 1 1 1 1 1 1 1 1 1 1 1 10 2 1 1 1 1 2 1 1 1 0 1 10 3 1 1 11 1 1 1 1 1 1 10 4 1 1 1 1 0 1 1 1 2 1 10 5 1 1 1 1 1 1 1 1 1 1 10 Sum 55 5 5 5 5 5 5 5 5Based on the first pass weighting factors in Table 7 and the normalizedTMP metrics in Table 5, first pass weighted FMP/T values can now becalculated. These are shown in Table 8.

TABLE 8 First Pass FMP Results Applications Wt FMP/T 1 21.64 2 14.01 322.45 4 21.70 5 17.50 (FMP/T)_(ras) 19.73

This process may then repeat 5 more times, in this example, to reduceall weighted FMP metrics to less than 20. The final usage weightingfactors are shown in Table 9, and the final weighted FMP results are inshown in Table 10.

TABLE 9 Six Pass Usage Weighting Factors Tools Applications 1 2 3 4 5 67 8 9 10 Sum 1 1 1 0 1 1 0 1 2 1 2 10 2 1 1 1 1 2 2 1 1 0 0 10 3 1 1 1 11 2 0 1 0 2 10 4 0 2 1 1 0 1 2 1 2 0 10 5 2 0 2 1 1 0 1 0 2 1 10 Sum 5 55 5 5 5 5 5 5 5

TABLE 10 Sixth Pass FMP Results Applications Wt FMP/T 1 19.62 2 13.32 319.29 4 18.89 5 13.89 (FMP/T)_(ras) 17.23

In this example, all of the resulting weighted FMP metrics have beenreduced to less than 20, and an overall normalized FMP metric has beenreduced from 20.13 to 17.23. Each value indicates improved fleetmatching.

It is also understood that in the above examples, there may be literallyhundreds or even thousands of applications, but in practice, thesenumbers can be reduced to a small number of families. For example, in asemiconductor device fabricator, the applications may be reduced to etchlinewidth-like measurements, resist contact hole-like measurements,spacewidth with embedded charge-like measurements, etc. Similarreductions may be possible in other manufacturers.

IV. Conclusion

As discussed herein, various systems and components are described as“obtaining” data (e.g., obtainer 130, etc.). It is understood that thecorresponding data can be obtained using any solution. For example, thecorresponding system/component can generate and/or be used to generatethe data, retrieve the data from one or more data stores (e.g., adatabase), receive the data from another system/component, and/or thelike. When the data is not generated by the particular system/component,it is understood that another system/component can be implemented apartfrom the system/component shown, which generates the data and providesit to the system/component and/or stores the data for access by thesystem/component.

While shown and described herein as a method and system for optimize afleet of measurement systems, it is understood that the inventionfurther provides various alternative embodiments. For example, in oneembodiment, the invention provides a program product stored on acomputer-readable medium, which when executed, enables a computerinfrastructure to optimize a fleet of measurement systems. To thisextent, the computer-readable medium includes program code, such asoptimization system 106 (FIG. 1), which implements the process describedherein. It is understood that the term “computer-readable medium”comprises one or more of any type of tangible medium of expression(e.g., physical embodiment) of the program code. In particular, thecomputer-readable medium can comprise program code embodied on one ormore portable storage articles of manufacture (e.g., a compact disc, amagnetic disk, a tape, etc.), on one or more data storage portions of acomputing device, such as memory 112 (FIG. 1) and/or storage system 122(FIG. 1) (e.g., a fixed disk, a read-only memory, a random accessmemory, a cache memory, etc.), as a data signal traveling over a network(e.g., during a wired/wireless electronic distribution of the programproduct), on paper (e.g., capable of being scanned in as electronicdata), and/or the like.

In another embodiment, the invention provides a method of generating asystem for optimize a fleet of measurement systems. In this case, acomputer infrastructure, such as computer infrastructure 102 (FIG. 1),can be obtained (e.g., created, maintained, having made available to,etc.) and one or more systems for performing the process describedherein can be obtained (e.g., created, purchased, used, modified, etc.)and deployed to the computer infrastructure. To this extent, thedeployment of each system can comprise one or more of: (1) installingprogram code on a computing device, such as computing device 104 (FIG.1), from a computer-readable medium; (2) adding one or more computingdevices to the computer infrastructure; and (3) incorporating and/ormodifying one or more existing systems of the computer infrastructure,to enable the computer infrastructure to perform the process steps ofthe invention.

In still another embodiment, the invention provides a business methodthat performs the process described herein on a subscription,advertising, and/or fee basis. That is, a service provider, such as anapplication service provider, could offer to optimize a fleet ofmeasurement systems as described herein. In this case, the serviceprovider can manage (e.g., create, maintain, support, etc.) a computerinfrastructure, such as computer infrastructure 102 (FIG. 1), thatperforms the process described herein for one or more customers. Inreturn, the service provider can receive payment from the customer(s)under a subscription and/or fee agreement, receive payment from the saleof advertising to one or more third parties, and/or the like.

As used herein, it is understood that the terms “program code” and“computer program code” are synonymous and mean any expression, in anylanguage, code or notation, of a set of instructions that cause acomputing device having an information processing capability to performa particular function either directly or after any combination of thefollowing: (a) conversion to another language, code or notation; (b)reproduction in a different material form; and/or (c) decompression. Tothis extent, program code can be embodied as one or more types ofprogram products, such as an application/software program, componentsoftware/a library of functions, an operating system, a basic I/Osystem/driver for a particular computing and/or I/O device, and thelike.

The foregoing description of various aspects of the invention has beenpresented for purposes of illustration and description. It is notintended to be exhaustive or to limit the invention to the precise formdisclosed, and obviously, many modifications and variations arepossible. Such modifications and variations that may be apparent to aperson skilled in the art are intended to be included within the scopeof the invention as defined by the accompanying claims.

1. A method of optimizing a fleet of measurement systems, the methodcomprising: obtaining an application tolerance (T) for each applicationto which at least one measurement system of the fleet is to be exposed;determining a tool matching precision (TMP) for each measurement systemin the fleet for each application to which a measurement system isexposed; and optimizing the fleet by: a) determining a usage weightingfactor (w_(ij)) for each measurement system (i) for each applicationrepresentative of a time the measurement system (i) spends performing aparticular application (j) and calculating at least one usageenforcement rule, b) calculating a weighted fleet measurement precision(FMP) metric for each application to which the fleet is exposed based onthe usage weighting factors, the weighted FMP metric equivalent to aroot average square of the TMP of each measurement system used for theapplication and weighted based on the usage weighting factors, c)calculating a normalized FMP metric, the normalized FMP metricequivalent to a root weighted average square of the weighted FMP metricdivided by the application tolerance across all applications, and d)re-assigning the usage weighting factors to minimize the normalized FMPmetric for all applications while enforcing the at least one usageenforcement rule.
 2. The method of claim 1, wherein the at least oneusage enforcement rule includes: $\begin{matrix}{{{\sum\limits_{j = 1}^{M}w_{ij}} = M_{i}},} & \left. a \right)\end{matrix}$ where M is a total number of applications and themeasurement system weight (M_(i)) represents a time spent by measurementsystem (i) performing all applications; and $\begin{matrix}{{{\sum\limits_{i = 1}^{N}w_{ij}} = N_{j}},} & \left. b \right)\end{matrix}$ where N is a total number of measurement systems in thefleet and application weight (N_(j)) represents a time spent by allmeasurement systems performing application (j).
 3. The method of claim1, wherein the at least one enforcement rule includes mandating that thenormalized FMP metric is less than a threshold.
 4. The method of claim1, wherein the optimizing further includes: calculating a normalized TMPmetric for each measurement system, the normalized TMP metric equivalentto the TMP of the measurement system for a particular applicationdivided by the application tolerance for the particular application; andidentifying at least one measurement system for one application toreduce the usage weighting factor based on the normalized TMP metrics.5. The method of claim 4, wherein the identifying includes: identifyingthe at least one exclusion measurement system based on the at least oneexclusion measurement system having a substantially dissimilarnormalized TMP metric compared to other measurement systems in thefleet; and wherein the assigning includes assigning the at least oneexclusion measurement system the usage weighting factor of zero.
 6. Themethod of claim 4, wherein the identifying includes: first identifying afirst application having an unacceptable weighted FMP metric and atarget measurement system used for the first application having anunacceptable normalized TMP metric when multiplied by a square root ofthe usage weighting factor, and wherein the assigning includesdecreasing the usage weighting factor by a weighting factor correctionfraction of a current usage weighting factor; second identifying asecond application for the target measurement system having anacceptable normalized TMP metric among the applications that the targetmeasurement system performs, and wherein the assigning includesadjusting the usage weighting factor for the target measurement systemfor the second application by adding the weighting factor correctionfraction; third identifying at least one compensating measurementsystems having a normalized TMP metric that is acceptable for the firstapplication and a normalized TMP metric that is higher for the secondapplication, and wherein the assigning includes distributing theweighting factor correction fraction as additions to the usage weightingfactors for the at least one compensating measurement system for thefirst application and as subtractions to the usage weighting factors forthe at least one compensating measurement system for the secondapplication in such a way as to enforce the enforcement rules.
 7. Themethod of claim 6, further comprising repeating the first, second andthird identifying.
 8. A system for optimizing a fleet of measurementsystems, the method comprising: an obtainer for obtaining an applicationtolerance (T) for each application to which at least one measurementsystem of the fleet is to be exposed; a tool matching precision (TMP)determinator for determining a tool matching precision (TMP) for eachmeasurement system in the fleet for each application to which ameasurement system is exposed; and an optimizer for optimizing thefleet, the optimizer including: a) a weight assigner for determining ausage weighting factor (w_(ij)) for each measurement system (i) for eachapplication representative of a time the measurement system (i) spendsperforming a particular application (j) and calculating at least oneusage enforcement rule, b) a fleet measurement precision (FMP)calculator for: i) calculating a weighted fleet measurement precision(FMP) metric for each application to which the fleet is exposed based onthe usage weighting factors, the weighted FMP metric equivalent to aroot average square of the TMP of each measurement system used for theapplication and weighted based on the usage weighting factors, and ii)calculating a normalized FMP metric, the normalized FMP metricequivalent to a root weighted average square of the weighted FMP metricdivided by the application tolerance across all applications; and c) aminimizer for invoking the weight assigner to re-assign the usageweighting factors to minimize the normalized FMP metric for allapplications while enforcing the at least one usage enforcement rule. 9.The system of claim 8, wherein the at least one usage enforcement ruleincludes: $\begin{matrix}{{{\sum\limits_{j = 1}^{M}w_{ij}} = M_{i}},} & \left. a \right)\end{matrix}$ where M is a total number of applications and themeasurement system weight (M_(i)) represents a time spent by measurementsystem (i) performing all applications; and $\begin{matrix}{{{\sum\limits_{i = 1}^{N}w_{ij}} = N_{j}},} & \left. b \right)\end{matrix}$ where N is a total number of measurement systems in thefleet and application weight (N_(j)) represents a time spent by allmeasurement systems performing application (j).
 10. The system of claim8, wherein the at least one enforcement rule mandates that thenormalized FMP metric is less than a threshold.
 11. The system of claim8, wherein the TMP calculator further calculates a normalized TMP metricfor each measurement system, the normalized TMP metric equivalent to theTMP of the measurement system for a particular application divided bythe application tolerance for the particular application; and furthercomprising an identifier for identifying at least one measurement systemfor one application to reduce the usage weighting factor based on thenormalized TMP metrics.
 12. The system of claim 11, wherein theidentifier identifies the at least one exclusion measurement systembased on the at least one exclusion measurement system having asubstantially dissimilar normalized TMP metric compared to othermeasurement systems in the fleet; and wherein the weight assignerassigns the at least one exclusion measurement system the usageweighting factor of zero.
 13. The system of claim 11, wherein theidentifier: first identifying a first application having an unacceptableweighted FMP metric and a target measurement system used for the firstapplication having an unacceptable normalized TMP metric when multipliedby a square root of the usage weighting factor, and wherein theassigning includes decreasing the usage weighting factor by a weightingfactor correction fraction of a current usage weighting factor; secondidentifying a second application for the target measurement systemhaving an acceptable normalized TMP metric among the applications thatthe target measurement system performs, and wherein the assigningincludes adjusting the usage weighting factor for the target measurementsystem for the second application by adding the weighting factorcorrection fraction; and third identifying at least one compensatingmeasurement systems having a normalized TMP metric that is acceptablefor the first application and a normalized TMP metric that is higher forthe second application, and wherein the assigning includes distributingthe weighting factor correction fraction as additions to the usageweighting factors for the at least one compensating measurement systemfor the first application and as subtractions to the usage weightingfactors for the at least one compensating measurement system for thesecond application in such a way as to enforce the enforcement rules.14. The system of claim 13, wherein the identifier repeats the first,second and third identifying.
 15. A program product stored on acomputer-readable medium, which when executed, optimizes a fleet ofmeasurement systems, the program product comprising: program code forobtaining an application tolerance (T) for each application to which atleast one measurement system of the fleet is to be exposed; program codefor determining a tool matching precision (TMP) for each measurementsystem in the fleet for each application to which a measurement systemis exposed; and program code for optimizing the fleet, the optimizingprogram code including: a) program code for determining a usageweighting factor (w_(ij)) for each measurement system (i) for eachapplication representative of a time the measurement system (i) spendsperforming a particular application (j) and calculating at least oneusage enforcement rule, b) program code for: i) calculating a weightedfleet measurement precision (FMP) metric for each application to whichthe fleet is exposed based on the usage weighting factors, the weightedFMP metric equivalent to a root average square of the TMP of eachmeasurement system used for the application and weighted based on theusage weighting factors, and ii) calculating a normalized FMP metric,the normalized FMP metric equivalent to a root weighted average squareof the weighted FMP metric divided by the application tolerance acrossall applications; and c) program code for invoking the weight assignerto re-assign the usage weighting factors to minimize the normalized FMPmetric for all applications while enforcing the at least one usageenforcement rule.
 16. The program product of claim 15, wherein the atleast one usage enforcement rule includes: $\begin{matrix}{{{\sum\limits_{j = 1}^{M}w_{ij}} = M_{j}},} & \left. a \right)\end{matrix}$ where M is a total number of applications and themeasurement system weight (M_(i)) represents a time spent by measurementsystem (i) performing all applications; and $\begin{matrix}{{{\sum\limits_{i = 1}^{N}w_{ij}} = N_{j}},} & \left. b \right)\end{matrix}$ where N is a total number of measurement systems in thefleet and application weight (N_(j)) represents a time spent by allmeasurement systems performing application (j).
 17. The program productof claim 15, wherein the TMP determining program code further calculatesa normalized TMP metric for each measurement system, the normalized TMPmetric equivalent to the TMP of the measurement system for a particularapplication divided by the application tolerance for the particularapplication; and the optimizing program code further includes: programcode for identifying at least one exclusion measurement system toexclude from the fleet based on the normalized TMP metrics.
 18. Theprogram product of claim 17, wherein the identifying program codeidentifies the at least one exclusion measurement system based on the atleast one exclusion measurement system having a substantially dissimilarnormalized TMP metric compared to other measurement systems in thefleet; and wherein the weight assigning program code assigns the atleast one exclusion measurement system the usage weighting factor ofzero.
 19. The program product of claim 17, wherein the identifyingprogram code: first identifying a first application having anunacceptable weighted FMP metric and a target measurement system usedfor the first application having an unacceptable normalized TMP metricwhen multiplied by a square root of the usage weighting factor, andwherein the assigning includes decreasing the usage weighting factor bya weighting factor correction fraction of a current usage weightingfactor; second identifying a second application for the targetmeasurement system having an acceptable normalized TMP metric among theapplications that the target measurement system performs, and whereinthe assigning includes adjusting the usage weighting factor for thetarget measurement system for the second application by adding theweighting factor correction fraction; and third identifying at least onecompensating measurement systems having a normalized TMP metric that isacceptable for the first application and a normalized TMP metric that ishigher for the second application, and wherein the assigning includesdistributing the weighting factor correction fraction as additions tothe usage weighting factors for the at least one compensatingmeasurement system for the first application and as subtractions to theusage weighting factors for the at least one compensating measurementsystem for the second application in such a way as to enforce theenforcement rules.
 20. The program product of claim 19, wherein theidentifying program code repeats the first, second and thirdidentifying.